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Evaluate : $\frac{\sin^3 60^\circ - \tan 30^\circ}{\cos^2 45^\circ}$
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Sol. $\frac{(\frac{\sqrt{3}}{2})^3 - \frac{1}{\sqrt{3}}}{(\frac{1}{\sqrt{2}})^2}$ (1/2 Mark)
= $\frac{\frac{3\sqrt{3}}{8} - \frac{1}{\sqrt{3}}}{\frac{1}{2}}$ (1/2 Mark)
= $\frac{\frac{9-8}{8\sqrt{3}}}{\frac{1}{2}}$ (1/2 Mark)
= $\frac{1}{8\sqrt{3}} \times 2 = \frac{1}{4\sqrt{3}}$ or $\frac{\sqrt{3}}{12}$ (1/2 Mark)
= $\frac{\frac{3\sqrt{3}}{8} - \frac{1}{\sqrt{3}}}{\frac{1}{2}}$ (1/2 Mark)
= $\frac{\frac{9-8}{8\sqrt{3}}}{\frac{1}{2}}$ (1/2 Mark)
= $\frac{1}{8\sqrt{3}} \times 2 = \frac{1}{4\sqrt{3}}$ or $\frac{\sqrt{3}}{12}$ (1/2 Mark)